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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 4, Pages 35–50 (Mi timm865)  

This article is cited in 2 scientific papers (total in 2 papers)

On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$

V. V. Arestovab, M. A. Filatovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Institute of Mathematics and Computer Science, Ural Federal University

Abstract: We give an upper bound for the error of the best approximation of the (first-order) differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$. This upper bound is close to a known lower bound and improves the previous upper bounds. To prove the upper estimate, we consider a specific family of operators; in this family, we choose an operator that provides the least bound for the error of the best approximation.

Keywords: Stechkin's problem, differential operator, half-line.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 284, suppl. 1, 24–40

Bibliographic databases:

UDC: 517.518+517.983
Received: 20.06.2012

Citation: V. V. Arestov, M. A. Filatova, “On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 35–50; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 24–40

Citation in format AMSBIB
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\by V.~V.~Arestov, M.~A.~Filatova
\paper On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 4
\pages 35--50
\mathnet{http://mi.mathnet.ru/timm865}
\elib{http://elibrary.ru/item.asp?id=18126466}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 284
\issue , suppl. 1
\pages 24--40
\crossref{https://doi.org/10.1134/S0081543814020035}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898717408}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Arestov V., Filatova M., “Best Approximation of the Differentiation Operator in the Space l-2 on the Semiaxis”, J. Approx. Theory, 187 (2014), 65–81  crossref  mathscinet  zmath  isi  elib  scopus
    2. Arestov V.V., Filatova M.A., “the Best Approximation of the Differentiation Operator By Linear Bounded Operators in the Space l (2) on the Semiaxis”, Dokl. Math., 90:2 (2014), 592–595  crossref  mathscinet  zmath  isi  elib  scopus
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